Try a restart or a reset before doing a restore. A reset in this instance is akin to rebooting a PC.
Restart - Press and hold the power off button, the one at the top right. You will see a slide appear to power off, slide this and the screen will go dark and a Whirly will appear. When the Whirly disappears your iPad is now off. Press the power button again until the Apple logo appears, this will take a few seconds and your iPad will restart. You should restart your iPad occasionally also as it will keep it running well. Now see if it is operating.
Reset - Hold the power off button and the home button simultaneously, keep holding them in and you will see the power off slide appear and disappear, wait until you see the Apple logo appear before releasing the buttons. It will take a little longer for your iPad to start.
This may also be a ram problem here, I'm thinking as your iPad is new you may have been downloading a lot of apps and such and also surfing the net quite a bit. Deleting your history and cookies will clear up more ram. Settings - Safari - Clear History and Cookies and Data.
Try all these and see how you go and let us know.
iPad 2 3G 64gb